Elliptic equations with critical exponent on a torus invariant region of 3

We study the multiplicity of positive solutions of a Brezis-Nirenberg-type problem on a region of the three-dimensional sphere, which is invariant by the natural torus action. In the paper by Brezis and Peletier, the case in which the region is invariant by the SO(3)-action is considered, namely, wh...

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Detalles Bibliográficos
Publicado: 2019
Materias:
Brezis-Nirenberg problem
Nonlinear elliptic equations
Yamabe equation
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_02191997_v21_n2_p_Rey
http://hdl.handle.net/20.500.12110/paper_02191997_v21_n2_p_Rey
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_02191997_v21_n2_p_Rey
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spelling paper:paper_02191997_v21_n2_p_Rey2023-06-08T15:21:35Z Elliptic equations with critical exponent on a torus invariant region of 3 Brezis-Nirenberg problem Nonlinear elliptic equations Yamabe equation We study the multiplicity of positive solutions of a Brezis-Nirenberg-type problem on a region of the three-dimensional sphere, which is invariant by the natural torus action. In the paper by Brezis and Peletier, the case in which the region is invariant by the SO(3)-action is considered, namely, when the region is a spherical cap. We prove that the number of positive solutions increases as the parameter of the equation tends to -∞, giving an answer to a particular case of an open problem proposed in the above referred paper. © 2019 World Scientific Publishing Company. 2019 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_02191997_v21_n2_p_Rey http://hdl.handle.net/20.500.12110/paper_02191997_v21_n2_p_Rey
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Brezis-Nirenberg problem
Nonlinear elliptic equations
Yamabe equation
spellingShingle Brezis-Nirenberg problem
Nonlinear elliptic equations
Yamabe equation
Elliptic equations with critical exponent on a torus invariant region of 3
topic_facet Brezis-Nirenberg problem
Nonlinear elliptic equations
Yamabe equation
description We study the multiplicity of positive solutions of a Brezis-Nirenberg-type problem on a region of the three-dimensional sphere, which is invariant by the natural torus action. In the paper by Brezis and Peletier, the case in which the region is invariant by the SO(3)-action is considered, namely, when the region is a spherical cap. We prove that the number of positive solutions increases as the parameter of the equation tends to -∞, giving an answer to a particular case of an open problem proposed in the above referred paper. © 2019 World Scientific Publishing Company.
title Elliptic equations with critical exponent on a torus invariant region of 3
title_short Elliptic equations with critical exponent on a torus invariant region of 3
title_full Elliptic equations with critical exponent on a torus invariant region of 3
title_fullStr Elliptic equations with critical exponent on a torus invariant region of 3
title_full_unstemmed Elliptic equations with critical exponent on a torus invariant region of 3
title_sort elliptic equations with critical exponent on a torus invariant region of 3
publishDate 2019
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_02191997_v21_n2_p_Rey
http://hdl.handle.net/20.500.12110/paper_02191997_v21_n2_p_Rey
_version_ 1768542835551764480

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